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OVERVALUING SMALL FRONT ROW PAIRS - Part II

March 13, 2014 - Part I covered setting small pairs early in the hand without proper backup. Now we will go over the same scenario, only later in the hand. This hand is heads up.


In this spot, the 3 of hearts could be set in the front to pair 3's. The rationale behind the play is usually one of the following:

1) Trying to win the front row
2) Trying for a scoop
3) Trying to avoid getting scooped
4) My opponent is going to foul, it's a freeroll

To help us understand why each one of these is incorrect, let's get the odds calculator out. The max number of outs left for a middle row pair after setting the 3 in front is 7. I will give the odds for 7 outs in this situation, as well as 6 and 5 outs, as it is likely that your opponent has one or two of your outs in their hand. The two percentages reflect in position/out of position.

Odds to pair the 7, 8 or A with 2 cards to come, 7 outs: 42% / 43%

Odds to pair the 7, 8 or A with 2 cards to come, 6 outs: 37% / 38%

Odds to pair the 7, 8 or A with 2 cards to come, 5 outs: 31% / 32%

The very best scenario here is under 50%, and it's quite likely that you'll be fouling 2 out of 3 times. With the math in hand, here's why all 4 of the above justifications are mistakes.

THE MISTAKE: Trying to win the front row.

THE ADVICE: You're supposed to win every row, or at least 2 of 3, right? In a perfect world, yes. But trying to win the front row here most likely leads to a foul, and more importantly it's a huge waste of the made flush, which adds both royalty and scoop equity to the hand. The difference between winning 2 of 3 rows or losing 2 of 3 is only a 2-point swing (+1 to -1). Fouling, however, is a 10-point swing, because not only do you lose your 4-point royalty equity but you go as far into the negative as you can in scoop equity (-6). Protecting the flush and hand equity accrued is optimal here.

THE MISTAKE: Trying for the scoop.

THE ADVICE: Greed is good in poker, and gambling is justified - when odds are in your favor. But going for the scoop in this spot is greedy beyond what the math and the hand contour allows. It's unreasonable to assume that even if the pair of 3's and the flush win the front and back that you will scoop here. If you did happen to go against the flow of probability and pair your 7 or 8 to unfoul, it's a medium strength pair with no guarantee of winning the row. Pairing the Ace specifically, which is more likely a middle row winner, is only a 13% / 14% favorite to hit (and that's with both Aces live). Getting the scoop would add 5-7 points, certainly not enough to justify a 7:1 risk. Selling earned equity in the hand at such a poor price is non-optimal.

THE MISTAKE: "Fouling and getting scooped are the same thing, so I might as well go for it"

THE ADVICE: This is one of the biggest misconceptions in the game and I can't tell you how many times I've heard this. The rationale behind this argument is that since the foul penalty is -6 points, and getting scooped is also -6 points (losing all three rows for 1 point each plus the 3 point scoop bonus), it is an exact equivalency that justifies (bad) gambling. But fouling and getting scooped are not equivalent when it comes to scoring. Here's the basic reason why:

When royalty equity is above 0 it always costs more to foul than to get scooped.

Royalties made in an unfouled hand will always count to the good and provide a defensive scoring buffer against your opponent regardless of how strong their hand is, even if you are scooped. However when you foul, your royalties are forfeit, so not only will you be paying the foul penalty but will have no royalty equity to offset that of your opponent.

The following chart looks at the 'Gamble Expected Value' of pairing the 3 at the very best odds where all 7 outs are live. Against the most common hands your opponent could be scoring royalties with, all four scoop equity situations are represented: scooping (+6), winning 2 of 3 rows (+1), losing 2 of 3 rows (-1), and getting scooped (-6). The hero's score is given for both an unfouled and a fouled hand in each scenario.

Every situation on the chart indicates a negative E.V. for the hand after pairing the 3's, even in the case of your opponent scooping you and having a better royalty (full house v. flush). Examining the 'Scooped' section in red shows a -4 point swing between fouling and getting scooped.



Obviously the stronger your overall equity position is, the more it costs to gamble, as the point swing numbers indicate. But contrary to what one might think at first glance, the E.V. of gambling gets WORSE the better your opponents' hand is, and that is due to the relative importance of royalty equity in the makeup of overall hand equity. So the idea that the stronger your opponents' hand is the harder you have to gamble is a fallacy when royalty equity is in positive territory.

THE MISTAKE: "My opponent is going to foul, it's a freeroll"

THE ADVICE: If you like lighting money on fire, gamble it up. In your very best scenario, you are scoring 0 points 58% of the time, and unfouling the rest of the time gets you only 4.25 points per hand over a sample size of 100. Or you could just not gamble and just take the guaranteed 10 points.

*Odds numbers in the chart are a synthesis of the in position and out of position numbers, as they differed by only 1%.

If you'd like to use our odds charts, they are free and can be accessed both on our site and as a PDF download.

ONLINE CHARTS HERE

PDF DOWNLOADS HERE
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